Pine wood

From a trunk of pine 6m long and 35 cm in diameter with a carved beam with a cross-section in the shape of a square so that the square had the greatest content area. Calculate the length of the sides of a square. Calculate the volume in cubic meters of lumber.

Correct result:

a =  24.7487 cm
V =  0.3675 m³

Solution:

$a=35\mathrm{/}\sqrt{2}=24.7487\text{ cm}$

$V=a^{2}h=0.247^2\cdot 6=0.3675{\text{m}}^3$

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